Raindrop spectra can be represented by an exponential function of the form:
N(D)=N_W exp(D/(D_0 ))
This equation predicts that the plots of Z against Z_DR for a constant N_W should lie on a well-defined curve; changes in N_W lead to proportionate changes in Z and thus a corresponding shift of the curves in the Z direction. Observations show that values of N_W in rain are fairly constant over 5 square km even though individual values of Z and rain rate, R, at each pixel are very variable. An efficient clutter removal algorithm using, for example the texture of differential phase shift, should remove the widely scattered Z and Z_DR pixels deemed to be clutter and leave the pixels classified as rain lying close to a constant N_W curve.
The value of a' in an empirical Z-R relationship of the form Z=aR^b' is inversely proportional to the square root of N_W. The objective analysis of the clutter removal algorithm proceeds as follows: following the clutter removal, the curve of best fit through the Z and Z_DR values gives an estimate of N_W, whilst the goodness of the fit provides an error in N_W. The best clutter removal algorithm is the one that gives the value of N_W with the lowest error. Too aggressive an algorithm will leave too few rainy pixels and a higher error in N_W; too forgiving an algorithm will accept clutter with noisy Z and Z_DR values and a higher error in N_W. Once the optimum N_W has been derived it can be used to define a more appropriate a' in the aforementioned Z-R relationship, allowing a better estimate of rainfall from each individual Z pixel.